具有质量聚集的随机介质中受驱粒子的中心极限定理

Local Central Limit Theorem for diffusions in a degenerate and unbounded Random Medium

We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for $X$, under some moment conditions on the environment; the key tool is a local parabolic Harnack inequality obtained with Moser iteration technique.

A central limit theorem for the Euler integral of a Gaussian random field

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural in the majority of applications, leads to a need for statistical analysis, the first step of which requires asymptotic distribution results for estimators. The first such result is provided in this paper, as a central limit theorem for the Euler integral of pure, Gaussian, noise fields.

修正大质量 Arratia 流的中心极限定理

A Central Limit Theorem for Modified Massive Arratia Flow

针对考虑质量聚集效应的修正大质量 Arratia 流，本文通过与可数多个独立 Brown 运动耦合获得关键混合估计，证明了均匀初始构型下簇位置点过程的中心极限定理。

A Low-rank Approximation for MDPs via Moment Coupling

We introduce a framework to approximate a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of optimality guarantees. The theory is grounded in recent work Braverman et al (2020} that relates the solution of the Bellman equation to that of a PDE where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments. Solving the PDE is $\textit{not}$ required by our method. Instead, we construct a "sister" …

池模型：一种质量守恒的多粒子聚并过程

Pool model: a mass preserving multi particle aggregation process

本文研究了二维空间中的池模型，该模型是多粒子扩散限制聚并（MDLA）的旋转对称类比。粒子在连续时间随机游走，并在进入圆形池时被吸收，从而增加池的质量并扩展池的面积，实现质量守恒。